Solution to Create Shadows and Blurring Images

I've recently been using Graphics.drawFilledPath to produced a background shadow effect. Although this function works flawlessly within JDE5 it does not provide the developer with the ability to apply a linear gradient with an Alpha Channel.

After doing some research and several hours of programming I've managed to produced a set of functions that provides a Gaussian Distribution Blur Filter. The function provided allows the user to blur an image with a given radius. It also allows the user to produce shadows.